1. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Self–Organized Service Management in
Heterogeneous and Dynamic MAS
M. Rebollo, E. del Val and V. Botti
Univ. Politecnica de Valencia (Spain)
9th European Workshop on Multi-Agent Systems
Maastricht, November 2011
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

2. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Self–Organized Service Management
The Problem
Automatic service self-adaption to the system demand without
global knowledge
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@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

3. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Our Proposal
The challenge
The introduction of the homophily concept improves the
performance of greedy local search algorithms and it can be used
as individual adaption criteria.
What is needed. . .
a network structure with small world characteristics
an efficient search algorithm
an adaptation mechanism to fit to the service demand
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

4. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Outline
1 Outline
2 System Definition
3 Homophily-based Network
4 Structural Homophily as Local Self-Adaptive Method
5 Discussion
6 Conclusions
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

5. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
System Definition
Homophily based network
Homophily
Tendency of individuals to associate and interact with similar ones
choice homophily: similarity measure
value homophily: shared attributes
status homophily: role
structural homophily: adaption to external conditions
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

6. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
System Definition
Network Model
Definition (System model)
(A, L), where
A = {a1 , ..., an } is a finite set of autonomous agents and
L ⊆ A × A is the set of links, where each link (ai , aj ) ∈ L
indicates the existence of a direct relationship between agent
ai and aj .
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

7. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
System Definition
Network Model
Definition (Agent)
An agent ai ∈ A = (Ri , Ni , sti , πi , ρi ), where:
Ri = {r1 , . . . , rm } is the set of roles played by the agent;
Ni is the set of neighbors of the agent,
Ni = {ap , ..., aq } : ∀aj ∈ Ni , ∃(ai , aj ) ∈ L, and |Ni | > 0.
It is assumed that |Ni | |A|;
sti is the internal state of the agent;
πi : sti → Ni , is the neighbor selection function that returns
the most promising neighbor to provide a service;
ρi : sti → Ψ is the adaptation selection function where Ψ is
the set of finite adaptation actions of the agent.
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

8. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
System Definition
Network Model
Definition (Role model)
A role ri ∈ Ri is defined by the tuple (φi , Si ) , where:
φi is a semantic concept for the role;
Si = {s1 , . . . , sl } is the set of services associated to the role.
Each service is defined by the tuple si = (Ii , Oi , Pi , Efi ), where
the components are the set of inputs, outputs, preconditions,
and effects of the services, respectively. All of them are
semantic concepts that can be defined in different ontologies.
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

9. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Value Homophily as Service Similarity
Definition (Value Homophily)
Hv (Si , Sj ) = α β ∗ WGI + (1 − β)WGO +
(1 − α) β ∗ WGP + (1 − β)WGEff =
wij ∈EI wij wij ∈EO wij
=α β + (1 − β) +
max |Ii |, |Ij | max |Oi |, |Oj |
wij ∈EP wij wij ∈EEf wij
+(1 − α) β + (1 − β)
max |Pi |, |Pj | max |Efi |, |Efj |
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

10. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Value Homophily as Service Similarity
!"## !"# !"## !"#
C1
C1 C4 C1 ω15 = 0.5 C4
C4 C1 0.5 C4
The value homophily function Hv (Si , Sj ) calculates the ω25 = 0.75
C2
degree of matching betweenC5
C2 C2
C5 two set of services, where S
C2 0.75 i
C5
C5
and Sj are the sets of services provided by the agents0.75 and ω = ai
C3C3
aj , respectively. In general, the C6 level of matching 36 0.75
C6 C3
C3 between to C6
C6
sets of semantic concepts Ci and Cj is calculated through a
G G
bipartite matching!graph. Let G = (Ci , Cj , E)G' = a( !"#,#!"# , E')
G = ( "## !",# E)
, be complete,
weighted, bipartite graph that links each concept ci ∈ Ci to
each concept cj with Cj . ωij values
Table ∈ the represents the weight associated
to the arc ei = "#! i , cj ) ∈ E between !i"#$%$&'()*'(+)*'(+),-.$%$'(/+$
! (c "$! "%! c and cj as the
semantic similarity between '()$! concepts. Four degrees of
"&! '()$! '($! those
ExpRandom ")! be'! identified: exact, subsumes, plug-in, and
matching can
Join(
'(*$! '!
fail [18]. The "+! match is considered as exact, if c1 ∈ Ci is
'($! '()$! '(*$!
!
equivalent to c2 ∈ Cj (c1 ≡ c2 ); subsumes, if c1 subsumes
@mrebollo UPV
c (c ❂ Service Management in Heterogeneous subsumed by c (c ❁ c );
Self–Organized c ); plug-in, if c is and Dynamic MAS

11. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Status Homophily as Role Similarity
Definition (Status Homophily)
Hs (Ri , Rj ) = max (rmatch(φi , φj ))
ri ∈Ri ,rj ∈Rj
where (Fu et al. 2009)

 1
 if path length = 0
rmatch(φi , φj ) = e (−λ(pl+pc)) ∗ δ if roles no siblings
 (−λ(pl−d))
 e ∗δ if roles siblings
and
e γdp − e −γdp
δ=
e γdp + e −γdp
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

12. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Status Homophily as Role Similarity
FilmRecommender
pl = 7
BookRecommender cp = 3
Recommender d=2
Leisure MusicRecommender superclasses = 3
superclasses = 4
LeisureOrganizer max depth = 6
TravelAgency
Informative HotelsManager
TouristInformation GeoInfo Location
PreparedFoodProvider WeatherMan
Food
Thing Supplier FoodProvider
FreshFoodProvider
Drink
Supplier Supplier CarSeller
VehicleSeller
CycleSeller
Seller CameraSeller
BookSeller
UniversityStaff
Occupational
Work Occupation SciencePublisher
Information
Publication NovelPublisher
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

13. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Community Creation
Definition (Choice Homophily)
CH(ai , aj ) = ϕ ∗ Hs (Ri , Rj ) + (1 − ϕ) ∗ Hv (Si , Sj )
The ϕ parameter regulates the importance of the influence of roles
(status homophily) or services (value homophily) in the total
homophily of the agent with its neighbors.
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

14. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Sample of Homophily-based Network Structure
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

15. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Homophily-based Network
Decentralized Service Search Algorithm
Neighbor selection function
πi (at ) = argmax Ps (aj , at )
aj ∈Ni
Where the probability for a neighbor to be chosen depends on its
similarity with the desired service (choice homophily) and its degree
|Nj |
CH(aj , at )
Ps (aj , at ) = 1 − 1 −
aj ∈Ni CH(aj , at )
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

16. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Structural Homophily as Local Self-Adaptive Method
Structural Homophily
Relative importance of an
agent based on the services it
has served and the queries it
has redirected as the value 1
0.9
agent traffic
fitted power-law function a*x^b
associated to the category ci 0.8
Number of received queries
of the most demanded service 0.7
0.6
si ∈ Si : 0.5
0.4
cib
0.3
SH(ai ) = a · 0.2
0.1
0 2 4 6 8 10 12 14 16
Category of the received queries
where
ci = argmax a · x b
x
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

17. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Structural Homophily as Local Self-Adaptive Method
Agent Self-Disconnection
Each agent decides
to leave the network if it is not important for the system
to replicate itself if it considers that it is relevant for the
network and it has received a significant increment in the
number of queries that it receives; or
to continue otherwise.
Probabilities for adaption function ρi
Pψ (leave) = 1 − SH(ai )
Pψ (continue) = Pψ (stay ∩ clone) = SH(ai )f (x )
Pψ (replicate) = Pψ (stay ∩ clone) = SH(ai )(1−f (x ))
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

18. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Structural Homophily as Local Self-Adaptive Method
Link Decay
1
n=2
n=4
The utility of the links decay 0.9
0.8
n=6
with time if they are not used 0.7
Probability to maintain the link
0.6
following a sigmoid function 0.5
0.4
1 0.3
dai (qi ) = 1 − −(qi −m)
0.2
0.1
1+l ·e n 0
0 10 20 30 40 50 60
Number of queries that were forwarded to other links
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

19. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Discussion
Search Performance
300 450
role-based EVN role-based EVN
EVN EVN
Random Random
Degree 400 Degree
250 Similarity Similarity
350
200 300
Number of paths
Number of paths
250
150
200
100 150
100
50
50
0 0
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100
Path length Path length
Search performance without role information (left) and combining
service and role information in the homophily calculation with
ϕ = 0.5 (right)
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

20. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Discussion
Agent Self-Disconnection
2500
Original network
self-adapted network
1
initial agents distribution
agents distribution
0.9 queries distribution 2000
0.8
0.7
Number of paths
1500
0.6
Agents
0.5
1000
0.4
0.3
500
0.2
0.1
0
0 0 10 20 30 40 50 60 70 80 90 100
0 2 4 6 8 10 12 14 16 18 Path length
Category
With agents deciding to stay, leave or clone, the network adapts to
the demand (left) and the average path length is reduced (right)
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

21. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Discussion
Link Decay
1 1600
initial agents distribution Original network
agents distribution self-adapted and rewired network
0.9 queries distribution
1400
0.8
1200
0.7
1000
Number of paths
0.6
800
Agents
0.5
600
0.4
400
0.3
200
0.2
0.1 0
0 -200
0 2 4 6 8 10 12 14 16 18 0 10 20 30 40 50 60 70 80 90 100
Category Path length
Including link decay, the network adapts to the demand (left) but
without significant changes in the path length (right).
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS

22. Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions
Conclusions
Conclusions
What we have done
network structure based on homophily as similarity criteria
greedy search algorithm with local information
adaption of the network without external coordination
agents decides to stay or to leave the system
link decay
Ongoing work: Non-cooperative agents
To include agents with different cooperation degree.
agents decide to remove links from non-cooperative agents
RF strategies to change the behavior to cooperate
@mrebollo UPV
Self–Organized Service Management in Heterogeneous and Dynamic MAS